Problem: Subtract the following rational expressions. $\dfrac{11y+9}{12y^3+4y}-\dfrac{3y^2+4}{12y^3+4y}=$
Solution: We want to subtract two rational expressions whose denominators are equal. We can do this by subtracting the numerators and keeping the denominator the same. [Does this fit with how we subtract rational numbers?] $\begin{aligned} &\phantom{=}\dfrac{11y+9}{12y^3+4y}-\dfrac{3y^2+4}{12y^3+4y} \\\\ &=\dfrac{(11y+9)-(3y^2+4)}{12y^3+4y} \\\\ &=\dfrac{11y+9-3y^2-4}{12y^3+4y} \\\\ &=\dfrac{-3y^2+11y+5}{12y^3+4y} \end{aligned}$ In conclusion, $\dfrac{11y+9}{12y^3+4y}-\dfrac{3y^2+4}{12y^3+4y}=\dfrac{-3y^2+11y+5}{12y^3+4y}$